Gary died on March $18,20$X$1.$ The estate tax year ends on December $31,20$X$1.$ The estate had the following items of income during the year: Interest $$250.$ Dividends $$150.$ Stock sale proceeds net of broker's commission $$10,000.$ Basis of the stock $$9,900.$ The estate made no distributions during $20$X$1.$ Which of the following statements regarding the requirement to file a Form $1041$ tax return is true?

The estate is not required to file an estate income tax return.

The estate is required to file an estate income tax return, because the estate made no distributions.

If the estate has expenses that reduce its income below $$600,$ no estate income tax return is required.

The estate is required to file an estate income tax return, because of the stock sale.